A simple model of the conformational transition between the right handed B double helix and the left handed Z double helix of DNA is proposed. This is a mechanistic model in which the dependence of the energy on twist is represented by two terms, one which depends upon the shape of the potential function through a series in powers of the twist and another inter-unit quadratic potential energy. This second term reflects the resistance of the DNA to deformations. With such a simple model we have studied cases of homogeneous chains with symmetric potential energies, as well as those within homogeneities and asymmetries in which one conformation is preferred over the other, for a portion of the chain. The method yields the location of the B-Z conformational boundaries for different conditions. Comparisons have been made with experiments in which G-C regions have been inserted in circular plasmid DNA.